A bridge across a valley is 150 m in

Question

length. The valley walls make angles of
60° and 54° with the bridge that spans it,
as shown. How deep is the valley, to the
nearest metre?

Answer 1

You have an Angle-Side-Angle triangle
draw an altitude to the 150 side
splitting that side into x and 150-x
I x is adjacent to 60°
tan60 = h/x
h = xtan60
also
tan 54 = h/(150-x)
h = (150-x)tan54

xtan60 = (150-x)tan54
xtan60 + xtan54 = 150tan54
x (tan60 + tan54) = 150tan54

solve for x, once you have x, sub into h = xtan60

Answer 2

A + b = 150 , D is the valley depth

tan(60º) = D / A ... A * tan(60º) = D

tan(54º) = D / (150 - A) ... [150 * tan(54º)] - [A * tan(60º)] = D

solve the system for A and D

Answer 3

You know that the third angle (call it A) is 180-60-54 = 66°
In triangle ABC, then, with side a=150, the height is

a sinB sinC/sinA = 150 * sin60° * sin54° / sin66° = 115

Answer 4

I dont understand this question please help me